Moving of an mirrored object does not give the desired outcome
In object mode, blender considers objects with mirror modifier a whole/complete object, just like a normal object. Therefore when you move it, you're moving the whole thing. However when you switch into edit mode, your mirror modifier start working as you edit, using the origin of the object as mirroring center pivot. Beware that the modifier will take object rotation into account, meaning it does not uses global axis as its mirroring pivot.